Article contents
REPRESENTING AN ELEMENT IN
${\mathbf{F} }_{q} [t] $ AS THE SUM OF TWO IRREDUCIBLES
Published online by Cambridge University Press: 23 May 2013
Abstract
A monic polynomial in ${\mathbf{F} }_{q} [t] $ of degree
$n$ over a finite field
${\mathbf{F} }_{q} $ of odd characteristic can be written as the sum of two irreducible monic elements in
${\mathbf{F} }_{q} [t] $ of degrees
$n$ and
$n- 1$ if
$q$ is larger than a bound depending only on
$n$. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable
$x$ with coefficients in
${\mathbf{F} }_{q} [t] $.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2013
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:39442:20160415013550641-0011:S0025579313000065_inline14.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:16564:20160415013550641-0011:S0025579313000065_inline15.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:45437:20160415013550641-0011:S0025579313000065_inline16.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:11213:20160415013550641-0011:S0025579313000065_inline17.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:83112:20160415013550641-0011:S0025579313000065_inline18.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:97480:20160415013550641-0011:S0025579313000065_inline19.gif?pub-status=live)
- 1
- Cited by